Just a note to record this citation by Jon Alan Schmidt of an important theme in Peirce. It touches on one of those recurring questions which has come up time and again on the Peirce List over the last twenty years, more acutely in recent Facebook discussions about universes of discourse, and more obliquely in the Ontolog Forum in connection with the AI/CogSci/DataBase issue of open vs. closed worlds. In another life, under another hat, I might have mentioned the Central Limit Theorem at this point as that would have brought us nearer Peirce’s core insight into the matter, but maybe another time …

JAS:

Every proposition is collective and copulative; as I stated in a recent post, its dynamical object is “the entire universe” (CP 5.448n, EP 2:394, 1906), which is “the totality of all real objects” (CP 5.152, EP 2:209, 1903), while its immediate object is “the logical universe of discourse” (CP 2.323, EP 2:283, 1903).

Thanks are due to JAS for calling attention to a critical point. I’m occupied with another train of thought at the moment so I’ll just stop to flag it for a later discussion. Incidentally, or synchronistically, lack of care in distinguishing different objects of the same signs, in particular, immediate and ultimate objects and their corresponding universes or object domains, has been the source of many misunderstandings in scattered discussions on Facebook of late.

Another issue arising here has to do with the difference between the “dimensionality of a relation” and the “number of correlates”. Signs may have any number of correlates in the object domain without requiring the dimensionality of the relevant sign relation to be greater than three. This is one of the consequences of “triadic relation irreducibility”.